Graphene-mediated exchange coupling between a molecular spin and magnetic substrates
S. Marocchi,1,2,*P. Ferriani,3N. M. Caffrey,3F. Manghi,1,2S. Heinze,3and V. Bellini2,4,†1Dipartimento di Fisica, Universit´a di Modena e Reggio Emilia, Via Campi 213/A, 41125 Modena, Italy 2S3-Istituto di Nanoscienze-CNR, Via Campi 213/A, 41125 Modena, Italy
3Instit¨ut f¨ur Theoretische Physik und Astrophysik, Christian-Albrecht-Universit¨at zu Kiel, Leibnizstrasse 15, 24098 Kiel, Germany 4Istituto di Struttura della Materia (ISM)-Consiglio Nazionale delle Ricerche (CNR), I-34149 Trieste, Italy
(Received 6 April 2013; published 8 October 2013)
Using first-principles calculations we demonstrate sizable exchange coupling between a magnetic molecule and a magnetic substrate via a graphene layer. As a model system we consider cobaltocene (CoCp2) adsorbed on graphene deposited on Ni(111). We find that the magnetic coupling is antiferromagnetic and is influenced by the molecule structure, the adsorption geometry, and the stacking of graphene on the substrate. We show how the coupling can be tuned by the intercalation of a magnetic monolayer, such as Fe or Co, between graphene and Ni(111). We identify the leading mechanism responsible for the coupling to be the spatial and energy matching of the frontier orbitals of CoCp2and graphene close to the Fermi level. Graphene plays the role of an electronic decoupling layer while allowing effective spin communication between molecule and substrate.
DOI:10.1103/PhysRevB.88.144407 PACS number(s): 71.15.Mb, 75.50.Xx, 68.43.−h, 81.05.ue
I. INTRODUCTION
The growing field of organic spintronics capitalizes on the novel functionalities achieved when organic molecules are adsorbed on magnetic substrates. The ability to manipulate and tune these functionalities is an important goal. Several problems remain, however, before such systems can be incor-porated into new technological devices. One in particular is the capability to adsorb magnetic molecules on surfaces without any detrimental effects being caused to either its structural or magnetic properties. It is thus vital to choose molecules with maximum structural robustness upon adsorption.1–3 To this end, the phthalocyanine (Pc) and porphyrin families are popular choices, due to their planar geometry.4–9 However, the strong interaction between the metal ion of such flat molecules and the substrate often modifies its electronic states and can even quench its magnetic moment.10 The use of nonplanar molecules, such as metallocenes, can minimize this effect. Metallocenes are composed of a 3d transition-metal ion sandwiched between two cyclopentadienyls (Cps). Depending on the metal ion species, both nonmagnetic and paramagnetic behavior can be found.11The spin of the metal ion is shielded from the surface by the cage formed by the two Cp rings, reducing the possibility that it will be modified substantially after adsorption.
Another viable route to further decrease an excessive interaction is the intercalation of a decoupling layer between the reactive surface and the molecule.3,12 Graphene is an attractive candidate in this regard, primarily due to the unique electronic properties that render it appealing for spintronic applications. It has already been successfully used to decouple Pc molecules from Ru(0001) and Ir(111) (Refs. 13 and
14) substrates. It is still an open question, however, if a graphene layer can preserve the magnetic properties of an adsorbed molecule without simultaneously hindering a stable magnetic coupling between the molecular moment and the magnetic substrate. Recent observations of charge transfer at molecule-graphene-Ni(111) interfaces15,16 would suggest that a magnetic coupling between a molecule and a substrate through a graphene layer is achievable.
In this work, we predict, by first-principles electronic structure methods, a sizable magnetic coupling for a mag-netic molecule adsorbed on a graphene layer deposited on a magnetic substrate, in this case Ni(111). We consider here cobaltocene (CoCp2), for which a theoretical prediction
of large charge transfer to graphene has been previously reported.17Furthermore, we propose intercalation of different ferromagnetic metal monolayers, such as Fe and Co, between graphene and the Ni substrate as a route to tailor the magnetic coupling. By comparing to the case where cobaltocene is directly adsorbed to Ni(111), we demonstrate that graphene is crucial to preserving the molecule magnetic moment and acts as an electronic decoupling layer, while allowing effective spin communication between molecule and substrate. Due to the unique electronic properties of graphene,18–20 metal-organic systems of this kind could serve as a basis for future spintronic devices.
II. RESULTS AND DISCUSSION
Density functional theory (DFT) calculations have been performed using the projector augmented wave method as implemented in the VASP code21,22 with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional.23 Disper-sion interactions have been included according to the DFT-D2 approach.24 Further computational details can be found in AppendixA.
Isolated CoCp2 has already been studied extensively by
DFT11 and several possible structures have been discussed. We consider here CoCp2 in the energetically lowest
high-symmetry configuration (D5h) where two possible Jahn-Teller
distorted structures characterized by two different electronic states occur (see AppendixB). The probability density of the highest occupied molecular orbital (HOMO) of both of these states, labeled2B2 and2A2, are plotted in Fig.1(a). In both
cases, the CoCp2molecule attains a nominal S = 1/2 spin.
The small lattice mismatch (1.2%) of graphene and Ni(111) lattice constant results in pseudomorphic growth and the flat conformation of the graphene layer.25 Our DFT calculations show that the bonding between graphene and the Ni(111)
FIG. 1. (Color online) (a) Probability density of the CoCp2 HOMO for the2A
2and2B2states. (b) top-fcc and bridge-top stacking of graphene on Ni(111) (the topmost, second, and third Ni layers are colored orange, yellow, and gray, respectively). (c) Adsorption geometries of the CoCp2on graphene/Ni(111) for the top-fcc stacking (Co, C, and H atoms in CoCp2are colored blue, dark gray, and white, respectively).
surface is primarily due to van der Waals (vdW) interactions, with a binding distance of 2.12 ˚A, in good agreement with experiments.26
We have taken into account several possible adsorption geometries CoCp2can assume on graphene/Ni(111), which we
labeled as hollow, bridge, and top, depending on the position of the Co atom with respect to the C atoms below [Fig.1(c)]. The results are presented in TableI, including the total energy difference E (with respect to the ground state), the Co (in the CoCp2molecule)-Ni distance d, and the exchange coupling
energies Eex, defined as Eex= EAP − EP, where EAP (EP)
is the total energy of the system when the spin moment of the Co atom is antiparallel (parallel) to the one of the Ni slab. Here a negative value of the exchange energy indicates that the cobaltocene’s spin moment preferentially orients antiparallel to the Ni magnetization. The lowest energy configuration (first row in TableI, configuration 1) is found when the molecule is adsorbed on the hollow site of graphene, which has a top-fcc stacking on the underlying Ni(111) substrate. The calculated adsorption energy of this configuration is∼0.64 eV,
TABLE I. Total energy difference E (meV), Co-graphene distance d ( ˚A), and exchange energy Eex(meV) for different structural and electronic configurations of CoCp2 on graphene/Ni(111); E are given in the case of antiparallel alignment of Co and Ni magnetic moments.
Configuration E d Eex
2B2, top-fcc, hollow 1 0.0 6.43 −9.7
2A2, top-fcc, hollow 2 +4.6 6.43 −1.3
2B2, top-fcc, bridge x 3 +55.2 6.42 −4.6 2B
2, top-fcc, bridge y 4 +74.8 6.43 −8.1 2B2, bridge-top, hollow 5 +105.2 6.41 −9.2
2B2, top-fcc, top 6 +147.9 6.52 −6.8
somewhere between those indicating physisorption and those indicating chemisorption (see Appendix B). A comparison of the total energies in Table I shows that, except for the case of configuration 2, all other configurations are strongly energetically unfavorable.
The magnetic ground state shows the molecular spin preferentially aligning antiparallel to the Ni magnetization, with Eexof the order of−10 meV. This energy is remarkably
large if we consider that the distance between the Co and Ni atoms is approximately 6.4 ˚A. As a comparison, an exchange energy of only 50 meV was found for chemisorbed Fe porphyrin on Co(100) (Ref.4), despite the much smaller Fe-Co distance of∼3.5 ˚A. The values of Eex that we find
are high enough to ensure the stability of the spin moments against temperature-induced fluctuations up to more than 100 K, i.e., well above the temperature of the order of a few Kelvins that is employed in state-of-the-art x-ray magnetic dichroism and spin-polarized scanning tunneling microscopy experiments.7,27
To elucidate the physical origin of the molecule-substrate exchange coupling we modify independently three possible contributions: the CoCp2electronic state, the graphene
stack-ing, and the CoCp2adsorption site. For the first we found that
switching from the2B2 to the2A2 electronic configurations
(configurations 1 and 2 in TableI) lowers the exchange energy from−9.7 to −1.3 meV. This considerable decrease can be attributed to the reduced extent of the CoCp2 spin-polarized
HOMO [see Fig.1(a)], which is critical to determining the size of the coupling. Varying the graphene stacking from top-fcc to bridge-top (configurations 1 and 5) does not influence the magnetic coupling in any appreciable way. This is somewhat surprising since the magnetic moment induced on graphene is approximately one order of magnitude smaller in the bridge-top than in the bridge-top-fcc stacking, with values of +0.002μB
and−0.03/+0.02μB, respectively. We can conclude therefore
that the magnetic coupling does not depend on the size of the magnetic moment induced on the graphene atoms. Finally, varying the adsorption site (configurations 1, 3, 4, and 6) can change Eexby up to a factor of two. However, the coupling
remains antiferromagnetic in all cases. The relaxed adsorption distance between the Co and Ni ions is similar for all the configurations of TableI, i.e., within 0.10 ˚A, and, therefore, cannot play a strong role in the differing exchange energies.
In Fig. 2 we present the spin-polarized local density of states (LDOS) of the system in its ground state (configuration
FIG. 2. (Color online) Spin-polarized LDOS of CoCp2 on graphene/M/Ni(111) in the antiparallel configuration, with M= Ni, Co and Fe: (a) 3d states of Co of CoCp2; (b)–(d) 3dz2 states
of the M layer atoms and 2pzstates of Ctopand Cfcc(for M= Ni)
or Ctopand Chcp(for M= Co, Fe; see text). The d states of the M layer are plotted in gray, while graphene C p states are in orange and dark green. Each curve in panels (b)–(d) is the average over the three atoms of that species closest to the CoCp2center. Inset in panel (a): 3d states of Co of CoCp2for the isolated molecule.
1). Majority (upper panels) and minority (lower panels) states are defined according to the magnetization of the Ni(111) substrate. Upon adsorption on the surface, we observe a small shift to higher energies of the molecular Co d orbitals with the result that the HOMO is pinned to the Fermi level (EF)
of the substrate. It also becomes partially depopulated. This is accompanied by a charge transfer of 0.28e− from the molecule to the surface and a decrease of the magnetic moment associated to the Co atom from +0.74μB to +0.47μB. A
hybridization between the 2pz orbital of the graphene atoms
and the 3dz2orbital of the Ni atom is also evident, resulting in
the polarization of graphene. Notably, only the Cfcc atoms
exhibit this strong hybridization with the Ni atoms close to EF. The energy overlap between the minority states of
graphene and the minority d states of CoCp2just below EF is
responsible for the stabilization of the antiparallel alignment. This energy matching is absent for the parallel alignment, due to the inverted HOMO spin polarization. We can thus conclude that the spin polarization of graphene close to EF determines
the sign of the magnetic coupling. This is further corroborated by the analogous situation occurring for configuration 5, for which both the graphene LDOS around EF and the magnetic
coupling are similar to the ones of configuration 1 [see Figs.3(a)and3(b)].
Such a dependence suggests that if one can modify the induced spin polarization of graphene in this energy window,
FIG. 3. (Color online) Spin-polarized LDOS at the C graphene atoms, close to the Fermi level (EF). (a) 2pz states of Ctop and
Cfcc atoms for configuration 1 of Table I. (b) 2pz states of the
only inequivalent C atom for configuration 5 of Table I. 2pz
states of Ctop and Chcp atoms for (c) graphene/Co/Ni(111) and (d) graphene/Fe/Ni(111). Each curve is the average over the three atoms of that species closest to the CoCp2 center. The Ctop and Cfcc/Chcp curves are colored red and blue, respectively.
one can modify the magnetic coupling. As a possible realiza-tion, we have explored the effect of intercalating different magnetic monolayers (Fe and Co) between graphene and the Ni(111) substrate. Experimentally, the intercalation of Ni and Co monolayers between graphene and Ir(111) (Refs.28
and29) and of Fe between graphene and Ni(111) (Ref.30) has been successfully achieved. As there are no experimental data for graphene/Co/Ni(111), we have used the same structure as for graphene/Fe/Ni(111), which allows for a direct comparison and therefore a clearer insight into the mechanism of the exchange interaction. As discussed in Ref.30, the intercalated Fe atoms are preferentially placed in the fcc hollow sites of the Ni, following the Ni(111) stacking. On this substrate, graphene adsorbs in a top-hcp structure, where the two inequivalent graphene C atoms are placed alternatively above the Fe atoms and the hcp sites, corresponding to the topmost Ni layer (see AppendixC).
We present in Figs.2(c)and2(d)the spin-polarized LDOS in the case of Fe and Co intercalation. The values of the corresponding magnetic moments and the exchange energies are listed in TableII. The magnitude of the spin moment in the interface metal (M) layer increases as one goes from Ni to Co to Fe and, due to hybridization, this increase also occurs for the moments induced on the C atoms, i.e., mtopC and mfcc
C .
TABLE II. Magnetic moments of the two nonequivalent atoms of graphene mtopC (μB) and m
fcc/hcp
C (μB), the interface metal monolayer
mM (μB), and the exchange energies Eex (meV) for CoCp2 on
graphene/M/Ni(111) (M= Ni, Co, Fe).
gr/Ni/Ni gr/Co/Ni gr/Fe/Ni
mtopC −0.02 −0.04 −0.05
mfcc/hcpC +0.03 +0.04 +0.04
mM +0.47 +1.52 +2.39
Surprisingly, the magnetic coupling is not found to increase in line with the magnetic moment and in fact decreases. We can identify a trend for the exchange energy between CoCp2and
the investigated substrate from large antiferromagnetic (Eex=
−9.7 meV) for graphene/Ni(111), to weak antiferromagnetic (Eex= −2.3 meV) for graphene/Co/Ni(111) and weak
fer-romagnetic (Eex= +2.0 meV) for graphene/Fe/Ni(111). The
energy matching between the HOMO of CoCp2 and the pz
states of the carbon atoms, which drives the coupling between the molecule and substrate, is disrupted by the intercalation of the metal layer. The minority dz2 states of the Co layer lie at
higher energies than those of Ni and the Fe states are found at even higher energies. Due to hybridization, the pzorbitals
of the graphene atoms are similarly shifted to higher energies. This reduces (for Co intercalation) and finally prevents (for Fe intercalation) the energy matching of the C states with the spin-polarized HOMO of CoCp2with a resultant decrease in
the magnetic coupling.
Figures 3(c) and 3(d) confirm this trend. For the graphene/Co/Ni(111) system, indeed the LDOS of the C atoms integrated in the region within 0.1 eV below EF in the
minority spin channel is somewhat larger than the one in the majority channel and so the matching with the CoCp2HOMO
FIG. 4. (Color online) Cross-sectional plots of the local magneti-zation density integrated from−0.1 eV to the Fermi level of CoCp2on (a) graphene/Ni(111) in top-fcc stacking, (b) graphene/Co/Ni(111), and (c) graphene/Fe/Ni(111). Left (right) panels refer to the parallel (antiparallel) configuration. The cross-sectional plane, indicated as purple broken line in Fig.1(c)(hollow adsorption site), cuts through the Co atom and is perpendicular to both the substrate and the Cp rings.
results in a small antiparallel coupling. On the other hand, for graphene/Fe/Ni(111) there is a slight excess of majority spin in the same energy range, which is consistent with the weak parallel coupling between the molecule and the substrate spins. Cross sectional plots of the magnetization density, i.e., the difference between the spin up and down charge densities, close to the Fermi level are given in Fig.4. In panel (a) the spatial matching of the CoCp2HOMO with the pzorbitals of
the Cfccatom of graphene adsorbed on Ni(111) is evident in
the antiparallel alignment where spin density lobes from the molecule and the surface atoms merge. In contrast, it is absent in the parallel alignment resulting in a negative exchange energy. For CoCp2 on graphene/Co/Ni [Fig.4(b)] there is an
excess of majority spin for the Ctop atoms and of minority
spin for the Chcp atoms which almost cancel each other.
However, a small preference towards communication through the minority spin is suggested by the plot in accordance with the weak antiferromagnetic coupling. For the Fe intercalated layer [Fig. 4(c)], the spin density in the graphene indicates spin communication for the parallel alignment, but not for the antiparallel alignment, explaining the positive exchange energy. The analysis performed for configuration 5 of TableI
(see Fig.5) reveals a scenario similar to the one of Fig.4(a)
and is consistent with an exchange coupling of similar size. To unambiguously determine the role of graphene in mediating the interaction between CoCp2 and the magnetic
substrate, we considered the situation when CoCp2is adsorbed
directly on the Ni(111) surface (see AppendixB). In this case, the molecule is chemisorbed with a distance between the Co and Ni atoms of d = 4.30 ˚A and an adsorption energy of ∼1.3 eV, i.e., about twice as large the one found in the presence of the graphene layer. Also the charge transfer from CoCp2to
Ni approximately doubles from 0.28 to 0.64 electrons if the spacing layer is removed. This indicates that graphene plays a crucial role in the electronic decoupling of the molecule and the substrate, and can facilitate the preservation of the structural integrity of such molecules upon deposition on metallic surfaces. As a matter of fact, it has been previously shown that deposition of metallocenes on metallic surfaces is a difficult process31 and can, in some cases, result in the complete dissociation of the molecule.32,33 Interestingly, the magnetic moment of cobaltocene is fully quenched when it is directly adsorbed on Ni(111). This clearly demonstrates that graphene is essential to preserve the magnetic properties of the molecule.
FIG. 5. (Color online) Cross-sectional plots of the local magne-tization density integrated from−0.1 eV to the Fermi level of CoCp2 on graphene/Ni(111) in bridge-top stacking. Left (right) panels refer to the parallel (antiparallel) configuration.
III. SUMMARY AND CONCLUSION
In conclusion, our work demonstrates that graphene plays a vital role in determining the interaction between a magnetic molecule and a ferromagnetic substrate. As a test case system in which to study these effects, we consider CoCp2 adsorbed
on a graphene layer grown on a magnetic Ni(111) substrate. We find that graphene behaves as an effective electronic decoupling layer yet allowing spin communication between the molecule and the substrate. The magnetic coupling is antiferromagnetic and the strength of the coupling can be ma-nipulated by changing the structural details of the adsorption. We also show that it is possible to tune the sign of the coupling by intercalating a magnetic monolayer between graphene and the Ni substrate.
Note added: Recently, Ref.34was published, where a study of the magnetic coupling between Co-octaethylporphyrin molecules and graphene/Ni(111) is presented.
ACKNOWLEDGMENTS
We thank Dr. Carlo Pignedoli for fruitful discussions. This work has been supported by FCRM “THE-SIMS,” the Deutsche Forschungsgemeinschaft via the SFB 677, the European Science Foundation (ESF) under the EUROCORES Program Euro-GRAPHENE, and the German Academic Ex-change Service (DAAD). We acknowledge the CINECA and HLRN centers for granting the high-performance computing resources.
APPENDIX A: COMPUTATIONAL DETAILS We performed preliminary calculations on a p(1× 1) hexagonal supercell to obtain geometry optimized graphene/M/Ni(111) (M= Ni, Co, Fe) structures and a density-of-states analysis of the systems. In this first part of our work we used a system containing one layer (two C atoms) of graphene and a four-layer metal slab. An optimized
-centered k-point grid of 17× 17 × 1 has been used for these small supercell calculations. The graphene layer and the top layer of metal were relaxed along the z axis. The three bottom layers of Ni were fixed at the bulk geometry with a lattice parameter of 2.49 ˚A that corresponds to the PBE bulk optimized Ni-Ni distance.
In order to verify the accuracy of this geometry we compared to a calculation in which the system has been modeled using the p(1× 1) unit cell with a six-layer metal slab and allowing the graphene layer and the three topmost layers of Ni to relax in all directions, i.e., four substrate layers have been fully relaxed. We found that the C-Ni distance changes as little as 0.001 ˚A as compared to the calculations reported in our article. The distance between the Ni surface and subsurface layers varies by 0.004 ˚A. The modification to the magnetic moments is only 0.002μBfor the C atoms and 0.019μBfor the
surface Ni atom, consistent with the tiny geometry variations. Such changes are minor and they do not affect the interaction between molecule and substrate, allowing us to use a four-layer rather than a six-layer Ni slab. The geometries of these small cells have been replicated in plane in order to build the bigger
p(5× 5) supercell containing not only the graphene-metal slab but also the CoCp2molecule. In this second set of calculations,
the graphene and metal layers were fixed and only the CoCp2
was fully relaxed. A -centered grid of 3× 3 × 1 k points has been used. Minimization proceeded until forces were lower than 0.01 eV ˚A−1.
We included in our calculations the vdW dispersion interactions. It is known that the nonlocal exchange-correlation energy functional (vdW-DF) results in an equilibrium distance between graphene and the topmost Ni layer larger than 3.5 ˚A (Ref. 35) for all the calculated structures, in disagreement with experiments. Thus, we employed the semiempirical potential DFT-D2 of Grimme.24With this method the estimate of the interaction energy is less reliable as compared to the vdW-DF; however, the typical errors never exceed 20% (Ref.24). On the other hand, the DFT-D2 gives trustworthy equilibrium distances. On average, the distances obtained with this method for small aromatic systems underestimate by about 5% the experimental values.24 In light of the fact that in our calculations it is essential to get the equilibrium distances as reliable as possible, we decided to use the semiempirical potential DFT-D2. Charge transfers were calculated using the Bader analysis.36
We checked the influence of an on-site Coulomb interaction on the exchange coupling energies Eex for the cases of
graphene/Ni(111) and graphene/Fe/Ni(111). Imposing static correlation effects on the d electrons of Co in CoCp2(values
of U− J = 2 and 4 eV have been tested), the magnetic coupling for CoCp2on graphene/Ni(111) changes from−9.7
to−10.5 meV while for the case of graphene/Fe/Ni(111) substrate it is not modified to any extent. We conclude that the employed GGA exchange correlation potential describes the magnetic properties of the investigated systems with sufficient accuracy.
APPENDIX B: COBALTOCENE ELECTRONIC STRUCTURE AND ADSORPTION ON Ni(111) AND
GRAPHENE/Ni(111)
We plot in Fig.6the two possible structures of a metallocene molecule, D5h and D5d, named after their point group
symmetry. In the former the two pentagons of the Cp rings are symmetric, while in the latter they are rotated by 180◦. Total energy calculations show that D5h symmetry is energetically
favored for isolated CoCp2molecules, with respect to D5d. The
FIG. 6. (Color online) (a) CoCp2in the symmetry configuration
D5h. (b) CoCp2 in the symmetry configuration D5d. Co, C, and H atoms in CoCp2are colored blue, gray, and white, respectively.
crystal field produced by the Cp rings split the 3d orbitals of Co. If we consider the axis of the molecule as our z axis, the seven 3d electrons are split in (i) two electrons in a singlet orbital derived from dz2, (ii) four electrons in a doubly
degenerate orbitals derived from dxy and dx2−y2, (iii) one
electron in a doubly degenerate orbitals derived from dyzand dxz. The D5hsymmetry is distorted to remove the degeneracy
of the frontier orbitals, according to the Jahn-Teller effect, so the symmetry is reduced to C2v. There are two possible
distortions and thus two possible electronic states; depending on whether the Cp rings tilt slightly toward the molecular center or outwards, the 2B2 or the 2A2 electronic states are
respectively produced, as shown in Fig.1(a). In the2B2state,
the HOMO has dyzcharacter while in the2A2state it has dxz
character.
The adsorption of CoCp2 on graphene/Ni(111) can be
regarded as strong physisorption as inferred from the fact that (i) the smallest distance between the H atoms of CoCp2 and
the C atoms of graphene is∼2.4 ˚A, (ii) there is no appreciable distortion of the structure of CoCp2 upon deposition on the
surface, and (iii) the C-C, C-Ni, and C-H bonds are nonpolar (or only weakly polar) excluding the formation of hydrogen bonds. The configuration where the CoCp2is oriented with its
axis perpendicular to the surface and in the top adsorption site, i.e., where the Co atom is directly above one of the graphene Ctop atom, is less stable than the configuration with the
CoCp2axis parallel to the substrate surface (configuration 1 in
Table I) by 40 meV. The minimum distance is 3.0 ˚A, as compared to 2.4 ˚A.
When the CoCp2is adsorbed directly on the Ni(111) surface
the magnetic moment of CoCp2 is fully quenched. This can
be recovered by rigidly shifting the molecule away from the surface by 1 ˚A, whereby the Co ion attains a magnetic moment of +0.26μB. As for the case including the graphene layer,
the magnetic coupling is antiparallel, albeit weakly (Eex=
−0.4 meV). A further rigid shift of the molecule by 1 ˚A results
FIG. 7. (Color online) (a) top-fcc stacking of graphene on Ni(111). (b) top-hcp stacking of graphene on M/Ni(111) (M= Fe, Co). The topmost, second, and third metal layers are colored orange, yellow, and gray, respectively.
in an increase of the Co magnetic moment to+0.35μB, while
the exchange coupling becomes negligibly small.
APPENDIX C: GRAPHENE STACKING FOR FE AND CO INTERCALATION
The surface lattice constant of the Ni(111) is 2.49 ˚A, with a very small lattice mismatch, i.e., 1.2%, with the one of graphene (2.46 ˚A). In the case of the intercalated Fe or Co monolayer, the lattice mismatch increases, yet a single layer is stable and does not lead to relevant modification in the graphene structure. The energetically favored top-fcc structure for graphene/Ni(111) (a) is compared with the top-hcp structure (b) attained for graphene/M/Ni(111), with
M= Fe and Co; first (topmost, orange), second (yellow), and
third (light gray) metallic layer atoms below graphene atoms (dark gray) are depicted in Fig.7. This figure was obtained usingVESTA(Ref.37). We found for graphene/Fe/Ni(111) and graphene/Co/Ni(111) a distance between graphene and the topmost metal layer of∼2.09 and ∼2.08 ˚A, respectively, close to the one of graphene/Ni(111).
*simone.marocchi@unimore.it
†valerio.bellini@unimore.it
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